deviance(setβ!(com05fe, β₀))
-
2491.15143905372542491.151439053724fit!(com05fe, β₀);
-
@@ -867,16 +867,16 @@ [ Info: (0, 2491.1514390537254)
-[ Info: (1, 2411.165742459929)
-[ Info: (2, 2409.382451337132)
-[ Info: (3, 2409.3774282835857)
+[ Info: (0, 2491.151439053724)
+[ Info: (1, 2411.1657424599252)
+[ Info: (2, 2409.3824513371324)
+[ Info: (3, 2409.3774282835834)
[ Info: (4, 2409.3774281600413)
@benchmark deviance(updateβ!(m)) seconds = 1 setup = (m = com05fe)
-BenchmarkTools.Trial: 10000 samples with 1 evaluation.
- Range (min … max): 67.528 μs … 161.118 μs ┊ GC (min … max): 0.00% … 0.00%
- Time (median): 76.638 μs ┊ GC (median): 0.00%
- Time (mean ± σ): 76.986 μs ± 2.640 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
+BenchmarkTools.Trial: 8774 samples with 1 evaluation.
+ Range (min … max): 108.750 μs … 186.792 μs ┊ GC (min … max): 0.00% … 0.00%
+ Time (median): 112.125 μs ┊ GC (median): 0.00%
+ Time (mean ± σ): 112.831 μs ± 4.958 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
- ▂▂▂▄▅▅▄▇██▆▅▄▄▅▅▄▃▂▂▂▂▂▁▁▁ ▂
- ▅▅▆▆▇▇▇▆▆▆▆▆▆▆▅▆▇▇▇██▇██████████████████████████████▇▇▇▇▇▇▇▇ █
- 67.5 μs Histogram: log(frequency) by time 84.5 μs <
+ ▁▇▂ █▄
+ ▃▃███▅▇██▅▃▂▃▃▂▂▁▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
+ 109 μs Histogram: frequency by time 139 μs <
- Memory estimate: 16.12 KiB, allocs estimate: 6.
+ Memory estimate: 16.25 KiB, allocs estimate: 6.
@@ -1052,14 +1052,14 @@ m = BernoulliPIRLS(com05.X, com05.y, only(com05.reterms).refs)
pdeviance(m)
-2409.377428160041
+2409.3774281600413
As with IRLS, the first iteration of PIRLS reduces the objective, which is the penalized deviance in this case, substantially.
pdeviance(updateu!(m))
-2233.1209476357844
+2233.120947635784
Create a pirls! method for this struct.
@@ -1094,25 +1094,25 @@
pirls!(m; verbose=true);
-[ Info: (0, 2409.377428160041)
-[ Info: (1, 2233.1209476357844)
-[ Info: (2, 2231.605935279706)
-[ Info: (3, 2231.6002198321576)
-[ Info: (4, 2231.600219406561)
+[ Info: (0, 2409.3774281600413)
+[ Info: (1, 2233.120947635784)
+[ Info: (2, 2231.6059352797056)
+[ Info: (3, 2231.600219832158)
+[ Info: (4, 2231.6002194065604)
As with IRLS, PIRLS is a fast and stable algorithm for determining the mode of the conditional distribution \(({\mathcal{U}}|{\mathcal{Y}}={\mathbf{y}})\) with \({\boldsymbol{\theta}}\) and \({\boldsymbol{\beta}}\) held fixed.
@benchmark pirls!(mm) seconds = 1 setup = (mm = m)
-BenchmarkTools.Trial: 4402 samples with 1 evaluation.
- Range (min … max): 199.693 μs … 331.599 μs ┊ GC (min … max): 0.00% … 0.00%
- Time (median): 227.186 μs ┊ GC (median): 0.00%
- Time (mean ± σ): 226.091 μs ± 5.569 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
+BenchmarkTools.Trial: 4847 samples with 1 evaluation.
+ Range (min … max): 197.708 μs … 325.792 μs ┊ GC (min … max): 0.00% … 0.00%
+ Time (median): 202.834 μs ┊ GC (median): 0.00%
+ Time (mean ± σ): 204.467 μs ± 10.549 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
- ▁ ▇█
- ▂▂▂▂▁▂▂▂▂▂▂▂▂▂▂▁▁▂▂▂▁▂▁▂▂▁▁▂▂▂▂▁▂▁▁▁▁▄█▄▄▃▂▃▃▃▃▃██▇▆▃▃▅▄▃▂▂▂▂ ▃
- 200 μs Histogram: frequency by time 234 μs <
+ ▆▃ ▄ ▃█
+ ██▄▆█▄██▃▆▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂▂▂▂▁▁▂▁▂▂▂▂▁▂▂▂▂▂▂▂▂▂▁▂▂ ▃
+ 198 μs Histogram: frequency by time 261 μs <
Memory estimate: 112 bytes, allocs estimate: 1.
@@ -1158,7 +1158,7 @@
laplaceapprox(pirls!(m))
-2373.518052752164
+2373.5180527521634
The remaining step is to optimize Laplace’s approximation to the GLMM deviance with respect to \(\theta\) and \({\boldsymbol{\beta}}\), which we do using the BOBYQA optimizer from NLopt.jl
@@ -1188,7 +1188,7 @@
fit!(m);
-[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 550, minf = 2354.4744815688055)
+[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 567, minf = 2354.474481568814)
@@ -1202,7 +1202,7 @@ )
-Converged to θ = 0.5683043594028967 and β =[-0.3409777149845993, 0.3933796201906975, 0.6064857599227369, -0.012926172564277872, 0.03323478854784157, -0.005626184982660486]
+Converged to θ = 0.5683043987329829 and β =[-0.3409777185006387, 0.39337972485653033, 0.606485842218137, -0.012926166672796164, 0.03323478753359014, -0.0056261864970479246]
These estimates differ somewhat from those for model com05.
@@ -1219,7 +1219,7 @@ )
-Estimates for com05: θ = 0.5761507901895634, fmin = 2353.8241980539815, and β =[-0.3414913998306781, 0.3936080536502067, 0.6064861079468472, -0.012911714642169572, 0.03321662487439253, -0.005625046845040066]
+Estimates for com05: θ = 0.5761302648250215, fmin = 2353.8241975646893, and β =[-0.3414688923098128, 0.3935941398175495, 0.6064453377878877, -0.012909611190401555, 0.03321034920788019, -0.0056245886330953615]
The discrepancy in the results is because the com05 results are based on a more accurate approximation to the integral called adaptive Gauss-Hermite Quadrature, which is discussed in Section C.6.
@@ -1304,10 +1304,10 @@ ev.values
5-element Vector{Float64}:
- -2.8569700138728
- -1.3556261799742608
- 1.3322676295501878e-15
- 1.3556261799742677
+ -2.8569700138728016
+ -1.3556261799742617
+ 8.881784197001252e-16
+ 1.3556261799742675
2.8569700138728056
@@ -1315,8 +1315,8 @@ abs2.(ev.vectors[1, :])
5-element Vector{Float64}:
- 0.011257411327720667
- 0.2220759220056134
+ 0.01125741132772062
+ 0.22207592200561319
0.5333333333333334
0.222075922005612
0.011257411327720648
@@ -1341,7 +1341,7 @@
-
+
Figure C.3: Change in the penalized deviance contribution from that at the conditional mode, for each of the first 5 groups, in model com05, as a function of u.
@@ -1616,7 +1616,7 @@
-
+
Figure C.6: Exponential of half the difference between the quadratic approximation and the contribution to the penalized deviance, for each of first 5 groups in model com05 as a function of z.
@@ -1667,20 +1667,20 @@
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
As we see, these “correction terms” relative to Laplace’s approximation are relatively small, compared to the contributions to the objective from each component of \({\mathbf{u}}\). Also, the corrections are all negative, in this case. Close examination of the individual curves in Figure C.5 shows that these curves, which are \(-2\log(f_j(z))\), are more-or-less odd functions, in the sense that the value at \(-z\) is approximately the negative of the value at \(z\). If we were integrating \(\log(f_j(z_j))\phi(z_j)\) with a normalized Gauss-Hermite rule the negative and positive values would cancel out, for the most part, and some of the integrals would be positive while others would be negative.
@@ -1729,24 +1729,24 @@ m.θβ
┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
+└ @ Main.Notebook ~/projects/EmbraceUncertainty/aGHQ.qmd:1212
┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
-[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 479, minf = 2353.82419755322)
+└ @ Main.Notebook ~/projects/EmbraceUncertainty/aGHQ.qmd:1212
+[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 502, minf = 2353.8241975532205)
7-element Vector{Float64}:
- 0.5761321679271924
- -0.3414655990254175
- 0.39359939391066806
- 0.6064447618771712
- -0.012909685721680265
- 0.03320994962034241
- -0.005624606329593786
+ 0.5761321943567461
+ -0.3414656014988162
+ 0.3935993795906205
+ 0.6064447386597025
+ -0.012909682389235384
+ 0.033209946254759815
+ -0.005624606286375493
-
This page was rendered from git revision 31e9b61
+This page was rendered from git revision 5657dd7
.
diff --git a/datatables.html b/datatables.html
index f618eee..16f8019 100644
--- a/datatables.html
+++ b/datatables.html
@@ -333,7 +333,9 @@
Tables.RowTable
-AbstractVector{T} where T<:NamedTuple (alias for AbstractArray{T, 1} where T<:NamedTuple)
+
+AbstractVector{T} where T<:NamedTuple (alias for AbstractArray{T, 1} where T<:NamedTuple)
+
The actual implementation of a row-table or column-table type may be different from these prototypes but it must provide access methods as if it were one of these types. Tables.jl provides the “glue” to treat a particular data table type as if it were row-oriented, by calling Tables.rows or Tables.rowtable on it, or column-oriented, by calling Tables.columntable on it.
@@ -343,7 +345,7 @@ TypedTables.jl
is a lightweight package (about 1500 lines of source code) that provides a concrete implementation of column-tables, called simply Table, as a NamedTuple of vectors.
A Table that is constructed from another type of column-table, such as an Arrow.Table or a DataFrame or an explicit NamedTuple of vectors, is simply a wrapper around the original table’s contents. On the other hand, constructing a Table from a row table first creates a ColumnTable, then wraps it.
-contratbl = Table(contra)
+contratbl = Table(contra)
Table with 5 columns and 1934 rows:
dist urban livch age use
@@ -369,7 +371,7 @@
-typeof(contratbl)
+typeof(contratbl)
Table{@NamedTuple{dist::String, urban::String, livch::String, age::Float64, use::String}, 1, @NamedTuple{dist::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, urban::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, livch::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, age::Arrow.DictEncoded{Float64, Int8, Arrow.Primitive{Float64, Vector{Float64}}}, use::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}}}
@@ -381,7 +383,7 @@
-contratbl.urban
+contratbl.urban
1934-element Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}:
"Y"
@@ -408,14 +410,14 @@ Symbols, not strings, usually typed as a : followed by the name, as shown in
-columnnames(contratbl)
+columnnames(contratbl)
(:dist, :urban, :livch, :age, :use)
The : form for creating the Symbol requires that the column name be a valid variable name in Julia. If, for example, a column name contains a blank, the : form must be replaced by an expression like var"<name>", which invokes what is called a “string macro”.
-contratbl.var"urban"
+contratbl.var"urban"
1934-element Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}:
"Y"
@@ -442,13 +444,13 @@
-contratbl[1]
+contratbl[1]
(dist = "D01", urban = "Y", livch = "3+", age = 18.44, use = "N")
-contratbl[2:5]
+contratbl[2:5]
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -466,7 +468,7 @@ A.3.2 A trivial example done several ways
Suppose we wish to select the rows from district D49 as a table. We could create a Boolean vector and use it to index into contratbl
-contratbl[contratbl.dist .== "D49"]
+contratbl[contratbl.dist .== "D49"]
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -495,8 +497,8 @@ .
-isD49dist(row) = row.dist == "D49" # a 'one-liner' function definition
-filter(isD49dist, contratbl)
+isD49dist(row) = row.dist == "D49" # a 'one-liner' function definition
+filter(isD49dist, contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -509,7 +511,7 @@
-filter(r -> r.dist == "D49", contratbl)
+filter(r -> r.dist == "D49", contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -522,7 +524,7 @@ .
-filter(==("D49") ∘ first, contratbl)
+filter(==("D49") ∘ first, contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -551,7 +553,7 @@ generator expression
-Table(r for r in contratbl if r.dist == "D49")
+Table(r for r in contratbl if r.dist == "D49")
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -565,10 +567,10 @@ Chapter 6 a newdata table is constructed from the Cartesian product of vectors of covariates as the newdata table.
-newdata = Table(
- (; age=a, ch=c, urban=u) # NamedTuple from iterator product
- for a in -10:3:20, c in [false, true], u in ["N", "Y"]
-)
+newdata = Table(
+ (; age=a, ch=c, urban=u) # NamedTuple from iterator product
+ for a in -10:3:20, c in [false, true], u in ["N", "Y"]
+)
Table with 3 columns and 44 rows:
age ch urban
@@ -607,7 +609,7 @@
In general a Tuple is written as a comma-separated set of values within parentheses.
-typeof((1, true, 'R'))
+typeof((1, true, 'R'))
Tuple{Int64, Bool, Char}
@@ -616,10 +618,10 @@
-newdata = Table(
- (; age, ch, urban) for age in -10:3:20, ch in [false, true],
- urban in ["N", "Y"]
-)
+newdata = Table(
+ (; age, ch, urban) for age in -10:3:20, ch in [false, true],
+ urban in ["N", "Y"]
+)
Table with 3 columns and 44 rows:
age ch urban
@@ -655,7 +657,7 @@ Chapter 6 we added a Boolean column, ch, indicating if livch is not "0", to the contra table using an expression like
-contratbl = Table(contratbl; ch=contratbl.livch .== "0")
+contratbl = Table(contratbl; ch=contratbl.livch .== "0")
Table with 6 columns and 1934 rows:
dist urban livch age use ch
@@ -682,9 +684,9 @@
-contratbl = Table(
- getproperties(contratbl, (:dist, :urban, :livch, :age, :use)),
-)
+contratbl = Table(
+ getproperties(contratbl, (:dist, :urban, :livch, :age, :use)),
+)
Table with 5 columns and 1934 rows:
dist urban livch age use
@@ -716,8 +718,8 @@ <
The JuliaData organization manages the development of several packages related to data science and data management, including DataFrames.jl, a comprehensive system for working with column-oriented data tables in Julia. Kamiński (2023), written by the primary author of that package, provides an in-depth introduction to data science facilities, in particular the DataFrames package, in Julia.
This package is particularly well-suited to more advanced data manipulation such as the split-apply-combine strategy (Wickham, 2011) and “joins” of data tables.
Bouchet-Valat & Kamiński (2023) compares the performance of DataFrames.jl to other data frame implementations in R and Python.
-This page was rendered from git revision 31e9b61
+This page was rendered from git revision 5657dd7
.
diff --git a/glmmbernoulli.html b/glmmbernoulli.html
index 25e5797..8cc1e20 100644
--- a/glmmbernoulli.html
+++ b/glmmbernoulli.html
@@ -534,18 +534,18 @@
(Intercept)
--0.0126
+-0.0125
0.1058
-0.12
-0.9052
+0.9061
0.4787
livch: 1
-0.1532
+0.1533
0.0982
1.56
-0.1188
+0.1185
@@ -558,7 +558,7 @@
livch: 3+
-0.2590
+0.2591
0.1022
2.53
0.0113
@@ -569,7 +569,7 @@ 0.0006
0.0095
0.07
-0.9466
+0.9479
@@ -582,7 +582,7 @@
urban: Y
-0.3770
+0.3771
0.0804
4.69
<1e-05
@@ -593,7 +593,7 @@ -0.0067
0.0069
-0.98
-0.3261
+0.3263
@@ -601,7 +601,7 @@ -0.0004
0.0007
-0.51
-0.6075
+0.6070
@@ -765,7 +765,7 @@
(Intercept)
--0.2194
+-0.2193
0.1155
-1.90
0.0576
@@ -784,7 +784,7 @@ 0.0035
0.0082
0.43
-0.6674
+0.6669
@@ -808,7 +808,7 @@ -0.0068
0.0069
-0.99
-0.3231
+0.3233
@@ -880,7 +880,7 @@
(Intercept)
--0.2302
+-0.2303
0.1140
-2.02
0.0434
@@ -888,7 +888,7 @@
urban: Y
-0.3461
+0.3462
0.0599
5.78
<1e-08
@@ -907,7 +907,7 @@ 0.0063
0.0078
0.80
-0.4249
+0.4247
@@ -1034,7 +1034,7 @@ -0.0131
0.0110
-1.19
-0.2351
+0.2352
@@ -1131,7 +1131,7 @@
ch: true
-0.6065
+0.6064
0.1045
5.80
<1e-08
@@ -1142,7 +1142,7 @@ -0.0129
0.0112
-1.16
-0.2470
+0.2471
@@ -1174,29 +1174,29 @@
Generalized Linear Mixed Model fit by maximum likelihood (nAGQ = 9)
use ~ 1 + urban + ch + age + :(abs2(age)) + ch & age + (1 | dist & urban)
- Distribution: Bernoulli{Float64}
- Link: LogitLink()
+ Distribution: Distributions.Bernoulli{Float64}
+ Link: GLM.LogitLink()
logLik deviance AIC AICc BIC
-1177.2418 2353.8242 2368.4836 2368.5418 2407.4550
Variance components:
Column Variance Std.Dev.
-dist & urban (Intercept) 0.331927 0.576131
+dist & urban (Intercept) 0.331929 0.576133
Number of obs: 1934; levels of grouping factors: 102
Fixed-effects parameters:
-─────────────────────────────────────────────────────────
- Coef. Std. Error z Pr(>|z|)
-─────────────────────────────────────────────────────────
-(Intercept) -0.341486 0.126906 -2.69 0.0071
-urban: Y 0.393595 0.0859086 4.58 <1e-05
-ch: true 0.606464 0.104531 5.80 <1e-08
-age -0.0129123 0.0111549 -1.16 0.2470
-abs2(age) -0.00562457 0.000844101 -6.66 <1e-10
-ch: true & age 0.0332117 0.0128228 2.59 0.0096
-─────────────────────────────────────────────────────────
+────────────────────────────────────────────────────────
+ Coef. Std. Error z Pr(>|z|)
+────────────────────────────────────────────────────────
+(Intercept) -0.341466 0.126905 -2.69 0.0071
+urban: Y 0.393594 0.0859087 4.58 <1e-05
+ch: true 0.606442 0.104529 5.80 <1e-08
+age -0.0129098 0.0111548 -1.16 0.2471
+abs2(age) -0.00562462 0.0008441 -6.66 <1e-10
+ch: true & age 0.0332098 0.0128227 2.59 0.0096
+────────────────────────────────────────────────────────
Notice that, although there are 60 distinct districts, there are only 102 distinct combinations of dist and urban represented in the data. In 15 of the 60 districts there are no rural women in the sample and in 3 districts there are no urban women in the sample, as shown in a frequency table
@@ -1307,23 +1307,23 @@ Table with 4 columns and 44 rows:
age ch urban η
┌─────────────────────────────
- 1 │ -10 false N -1.44276
- 2 │ -7 false N -1.29428
- 3 │ -4 false N -1.24704
- 4 │ -1 false N -1.30104
- 5 │ 2 false N -1.45629
- 6 │ 5 false N -1.71278
- 7 │ 8 false N -2.07051
- 8 │ 11 false N -2.52948
- 9 │ 14 false N -3.0897
- 10 │ 17 false N -3.75115
- 11 │ 20 false N -4.51385
- 12 │ -10 true N -0.894068
- 13 │ -7 true N -0.546316
- 14 │ -4 true N -0.299807
- 15 │ -1 true N -0.15454
+ 1 │ -10 false N -1.44277
+ 2 │ -7 false N -1.29427
+ 3 │ -4 false N -1.24702
+ 4 │ -1 false N -1.30101
+ 5 │ 2 false N -1.45624
+ 6 │ 5 false N -1.71271
+ 7 │ 8 false N -2.07043
+ 8 │ 11 false N -2.5294
+ 9 │ 14 false N -3.0896
+ 10 │ 17 false N -3.75105
+ 11 │ 20 false N -4.51374
+ 12 │ -10 true N -0.89408
+ 13 │ -7 true N -0.546324
+ 14 │ -4 true N -0.299812
+ 15 │ -1 true N -0.154542
16 │ 2 true N -0.110516
- 17 │ 5 true N -0.167734
+ 17 │ 5 true N -0.167733
⋮ │ ⋮ ⋮ ⋮ ⋮
@@ -1346,7 +1346,7 @@
-
+
Figure 6.3: Linear predictor versus centered age from model com05
@@ -1411,23 +1411,23 @@ <
Table with 5 columns and 44 rows:
age ch urban η μ
┌────────────────────────────────────────
- 1 │ -10 false N -1.44276 0.191118
- 2 │ -7 false N -1.29428 0.215129
- 3 │ -4 false N -1.24704 0.223213
- 4 │ -1 false N -1.30104 0.213989
- 5 │ 2 false N -1.45629 0.189035
- 6 │ 5 false N -1.71278 0.152804
- 7 │ 8 false N -2.07051 0.111996
- 8 │ 11 false N -2.52948 0.0738171
- 9 │ 14 false N -3.0897 0.0435342
- 10 │ 17 false N -3.75115 0.0229515
- 11 │ 20 false N -4.51385 0.0108374
- 12 │ -10 true N -0.894068 0.290271
- 13 │ -7 true N -0.546316 0.366719
- 14 │ -4 true N -0.299807 0.425605
- 15 │ -1 true N -0.15454 0.461442
+ 1 │ -10 false N -1.44277 0.191117
+ 2 │ -7 false N -1.29427 0.215131
+ 3 │ -4 false N -1.24702 0.223217
+ 4 │ -1 false N -1.30101 0.213996
+ 5 │ 2 false N -1.45624 0.189043
+ 6 │ 5 false N -1.71271 0.152812
+ 7 │ 8 false N -2.07043 0.112004
+ 8 │ 11 false N -2.5294 0.073823
+ 9 │ 14 false N -3.0896 0.0435383
+ 10 │ 17 false N -3.75105 0.0229538
+ 11 │ 20 false N -4.51374 0.0108386
+ 12 │ -10 true N -0.89408 0.290269
+ 13 │ -7 true N -0.546324 0.366718
+ 14 │ -4 true N -0.299812 0.425604
+ 15 │ -1 true N -0.154542 0.461441
16 │ 2 true N -0.110516 0.472399
- 17 │ 5 true N -0.167734 0.458164
+ 17 │ 5 true N -0.167733 0.458165
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮
@@ -1450,7 +1450,7 @@ <
-
+
Figure 6.5: Predicted probability of contraception use versus centered age from model com05.
@@ -1466,10 +1466,10 @@ <
Table with 5 columns and 4 rows:
age ch urban η μ
┌───────────────────────────────────────
- 1 │ 2 false N -1.45629 0.189035
+ 1 │ 2 false N -1.45624 0.189043
2 │ 2 true N -0.110516 0.472399
- 3 │ 2 false Y -0.669101 0.338698
- 4 │ 2 true Y 0.676673 0.662996
+ 3 │ 2 false Y -0.669052 0.338709
+ 4 │ 2 true Y 0.676672 0.662995
The predicted probability of woman with centered age of 2, with children, living in an urban environment using artificial contraception is about 2/3, which is reasonably close to the smoothed frequency for that combination of covariates in Figure 6.2.
@@ -1487,7 +1487,7 @@
-
+
Figure 6.6: Caterpillar plot of the conditional modes of the random-effects for model com05
@@ -1506,12 +1506,12 @@ Table with 2 columns and 6 rows:
dist & urban (Intercept)
┌──────────────────────────
- 1 │ ("D01", "N") -0.957366
- 2 │ ("D11", "N") -0.93198
- 3 │ ("D24", "N") -0.603418
+ 1 │ ("D01", "N") -0.957367
+ 2 │ ("D11", "N") -0.931983
+ 3 │ ("D24", "N") -0.60342
4 │ ("D01", "Y") -0.580203
- 5 │ ("D27", "N") -0.576647
- 6 │ ("D55", "Y") -0.548261
+ 5 │ ("D27", "N") -0.576648
+ 6 │ ("D55", "Y") -0.548263
@@ -1520,12 +1520,12 @@ Table with 2 columns and 6 rows:
dist & urban (Intercept)
┌──────────────────────────
- 1 │ ("D43", "N") 0.64408
- 2 │ ("D04", "Y") 0.644669
- 3 │ ("D42", "N") 0.665114
- 4 │ ("D58", "N") 0.677418
+ 1 │ ("D43", "N") 0.644081
+ 2 │ ("D04", "Y") 0.644671
+ 3 │ ("D42", "N") 0.665117
+ 4 │ ("D58", "N") 0.67742
5 │ ("D14", "Y") 0.695322
- 6 │ ("D34", "N") 1.08591
+ 6 │ ("D34", "N") 1.08592
The largest random effect is for rural settings in D34. There were 26 women in the sample from rural D34
@@ -1565,12 +1565,12 @@
exp(last(first(srtdre)))
-0.38390287360272524
+0.3839023558380497
or about 40%.
-This page was rendered from git revision 31e9b61
+This page was rendered from git revision 5657dd7
.
diff --git a/index.html b/index.html
index f8ffd96..0ed055f 100644
--- a/index.html
+++ b/index.html
@@ -9,7 +9,7 @@
-
+
Embrace Uncertainty
@benchmark deviance(updateβ!(m)) seconds = 1 setup = (m = com05fe)BenchmarkTools.Trial: 10000 samples with 1 evaluation.
- Range (min … max): 67.528 μs … 161.118 μs ┊ GC (min … max): 0.00% … 0.00%
- Time (median): 76.638 μs ┊ GC (median): 0.00%
- Time (mean ± σ): 76.986 μs ± 2.640 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
+BenchmarkTools.Trial: 8774 samples with 1 evaluation.
+ Range (min … max): 108.750 μs … 186.792 μs ┊ GC (min … max): 0.00% … 0.00%
+ Time (median): 112.125 μs ┊ GC (median): 0.00%
+ Time (mean ± σ): 112.831 μs ± 4.958 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
- ▂▂▂▄▅▅▄▇██▆▅▄▄▅▅▄▃▂▂▂▂▂▁▁▁ ▂
- ▅▅▆▆▇▇▇▆▆▆▆▆▆▆▅▆▇▇▇██▇██████████████████████████████▇▇▇▇▇▇▇▇ █
- 67.5 μs Histogram: log(frequency) by time 84.5 μs <
+ ▁▇▂ █▄
+ ▃▃███▅▇██▅▃▂▃▃▂▂▁▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
+ 109 μs Histogram: frequency by time 139 μs <
- Memory estimate: 16.12 KiB, allocs estimate: 6.
+ Memory estimate: 16.25 KiB, allocs estimate: 6.m = BernoulliPIRLS(com05.X, com05.y, only(com05.reterms).refs)
pdeviance(m)
-
2409.3774281600412409.3774281600413As with IRLS, the first iteration of PIRLS reduces the objective, which is the penalized deviance in this case, substantially.
pdeviance(updateu!(m))
-
2233.12094763578442233.120947635784Create a pirls! method for this struct.
pirls!(m; verbose=true);
-[ Info: (0, 2409.377428160041)
-[ Info: (1, 2233.1209476357844)
-[ Info: (2, 2231.605935279706)
-[ Info: (3, 2231.6002198321576)
-[ Info: (4, 2231.600219406561)
+[ Info: (0, 2409.3774281600413)
+[ Info: (1, 2233.120947635784)
+[ Info: (2, 2231.6059352797056)
+[ Info: (3, 2231.600219832158)
+[ Info: (4, 2231.6002194065604)
As with IRLS, PIRLS is a fast and stable algorithm for determining the mode of the conditional distribution \(({\mathcal{U}}|{\mathcal{Y}}={\mathbf{y}})\) with \({\boldsymbol{\theta}}\) and \({\boldsymbol{\beta}}\) held fixed.
@benchmark pirls!(mm) seconds = 1 setup = (mm = m)
-BenchmarkTools.Trial: 4402 samples with 1 evaluation.
- Range (min … max): 199.693 μs … 331.599 μs ┊ GC (min … max): 0.00% … 0.00%
- Time (median): 227.186 μs ┊ GC (median): 0.00%
- Time (mean ± σ): 226.091 μs ± 5.569 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
+BenchmarkTools.Trial: 4847 samples with 1 evaluation.
+ Range (min … max): 197.708 μs … 325.792 μs ┊ GC (min … max): 0.00% … 0.00%
+ Time (median): 202.834 μs ┊ GC (median): 0.00%
+ Time (mean ± σ): 204.467 μs ± 10.549 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
- ▁ ▇█
- ▂▂▂▂▁▂▂▂▂▂▂▂▂▂▂▁▁▂▂▂▁▂▁▂▂▁▁▂▂▂▂▁▂▁▁▁▁▄█▄▄▃▂▃▃▃▃▃██▇▆▃▃▅▄▃▂▂▂▂ ▃
- 200 μs Histogram: frequency by time 234 μs <
+ ▆▃ ▄ ▃█
+ ██▄▆█▄██▃▆▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂▂▂▂▁▁▂▁▂▂▂▂▁▂▂▂▂▂▂▂▂▂▁▂▂ ▃
+ 198 μs Histogram: frequency by time 261 μs <
Memory estimate: 112 bytes, allocs estimate: 1.
@@ -1158,7 +1158,7 @@
laplaceapprox(pirls!(m))
-2373.518052752164
+2373.5180527521634
The remaining step is to optimize Laplace’s approximation to the GLMM deviance with respect to \(\theta\) and \({\boldsymbol{\beta}}\), which we do using the BOBYQA optimizer from NLopt.jl
@@ -1188,7 +1188,7 @@
fit!(m);
-[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 550, minf = 2354.4744815688055)
+[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 567, minf = 2354.474481568814)
@@ -1202,7 +1202,7 @@ )
-Converged to θ = 0.5683043594028967 and β =[-0.3409777149845993, 0.3933796201906975, 0.6064857599227369, -0.012926172564277872, 0.03323478854784157, -0.005626184982660486]
+Converged to θ = 0.5683043987329829 and β =[-0.3409777185006387, 0.39337972485653033, 0.606485842218137, -0.012926166672796164, 0.03323478753359014, -0.0056261864970479246]
These estimates differ somewhat from those for model com05.
@@ -1219,7 +1219,7 @@ )
-Estimates for com05: θ = 0.5761507901895634, fmin = 2353.8241980539815, and β =[-0.3414913998306781, 0.3936080536502067, 0.6064861079468472, -0.012911714642169572, 0.03321662487439253, -0.005625046845040066]
+Estimates for com05: θ = 0.5761302648250215, fmin = 2353.8241975646893, and β =[-0.3414688923098128, 0.3935941398175495, 0.6064453377878877, -0.012909611190401555, 0.03321034920788019, -0.0056245886330953615]
The discrepancy in the results is because the com05 results are based on a more accurate approximation to the integral called adaptive Gauss-Hermite Quadrature, which is discussed in Section C.6.
@@ -1304,10 +1304,10 @@ ev.values
5-element Vector{Float64}:
- -2.8569700138728
- -1.3556261799742608
- 1.3322676295501878e-15
- 1.3556261799742677
+ -2.8569700138728016
+ -1.3556261799742617
+ 8.881784197001252e-16
+ 1.3556261799742675
2.8569700138728056
@@ -1315,8 +1315,8 @@ abs2.(ev.vectors[1, :])
5-element Vector{Float64}:
- 0.011257411327720667
- 0.2220759220056134
+ 0.01125741132772062
+ 0.22207592200561319
0.5333333333333334
0.222075922005612
0.011257411327720648
@@ -1341,7 +1341,7 @@
-
+
Figure C.3: Change in the penalized deviance contribution from that at the conditional mode, for each of the first 5 groups, in model com05, as a function of u.
@@ -1616,7 +1616,7 @@
-
+
Figure C.6: Exponential of half the difference between the quadratic approximation and the contribution to the penalized deviance, for each of first 5 groups in model com05 as a function of z.
@@ -1667,20 +1667,20 @@
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
As we see, these “correction terms” relative to Laplace’s approximation are relatively small, compared to the contributions to the objective from each component of \({\mathbf{u}}\). Also, the corrections are all negative, in this case. Close examination of the individual curves in Figure C.5 shows that these curves, which are \(-2\log(f_j(z))\), are more-or-less odd functions, in the sense that the value at \(-z\) is approximately the negative of the value at \(z\). If we were integrating \(\log(f_j(z_j))\phi(z_j)\) with a normalized Gauss-Hermite rule the negative and positive values would cancel out, for the most part, and some of the integrals would be positive while others would be negative.
@@ -1729,24 +1729,24 @@ m.θβ
┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
+└ @ Main.Notebook ~/projects/EmbraceUncertainty/aGHQ.qmd:1212
┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
-[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 479, minf = 2353.82419755322)
+└ @ Main.Notebook ~/projects/EmbraceUncertainty/aGHQ.qmd:1212
+[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 502, minf = 2353.8241975532205)
7-element Vector{Float64}:
- 0.5761321679271924
- -0.3414655990254175
- 0.39359939391066806
- 0.6064447618771712
- -0.012909685721680265
- 0.03320994962034241
- -0.005624606329593786
+ 0.5761321943567461
+ -0.3414656014988162
+ 0.3935993795906205
+ 0.6064447386597025
+ -0.012909682389235384
+ 0.033209946254759815
+ -0.005624606286375493
-
pirls!(m; verbose=true);[ Info: (0, 2409.377428160041)
-[ Info: (1, 2233.1209476357844)
-[ Info: (2, 2231.605935279706)
-[ Info: (3, 2231.6002198321576)
-[ Info: (4, 2231.600219406561)[ Info: (0, 2409.3774281600413)
+[ Info: (1, 2233.120947635784)
+[ Info: (2, 2231.6059352797056)
+[ Info: (3, 2231.600219832158)
+[ Info: (4, 2231.6002194065604)@benchmark pirls!(mm) seconds = 1 setup = (mm = m)
-
@@ -1158,7 +1158,7 @@ BenchmarkTools.Trial: 4402 samples with 1 evaluation.
- Range (min … max): 199.693 μs … 331.599 μs ┊ GC (min … max): 0.00% … 0.00%
- Time (median): 227.186 μs ┊ GC (median): 0.00%
- Time (mean ± σ): 226.091 μs ± 5.569 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
+BenchmarkTools.Trial: 4847 samples with 1 evaluation.
+ Range (min … max): 197.708 μs … 325.792 μs ┊ GC (min … max): 0.00% … 0.00%
+ Time (median): 202.834 μs ┊ GC (median): 0.00%
+ Time (mean ± σ): 204.467 μs ± 10.549 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
- ▁ ▇█
- ▂▂▂▂▁▂▂▂▂▂▂▂▂▂▂▁▁▂▂▂▁▂▁▂▂▁▁▂▂▂▂▁▂▁▁▁▁▄█▄▄▃▂▃▃▃▃▃██▇▆▃▃▅▄▃▂▂▂▂ ▃
- 200 μs Histogram: frequency by time 234 μs <
+ ▆▃ ▄ ▃█
+ ██▄▆█▄██▃▆▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂▂▂▂▁▁▂▁▂▂▂▂▁▂▂▂▂▂▂▂▂▂▁▂▂ ▃
+ 198 μs Histogram: frequency by time 261 μs <
Memory estimate: 112 bytes, allocs estimate: 1.
laplaceapprox(pirls!(m))
-2373.518052752164
+2373.5180527521634
laplaceapprox(pirls!(m))2373.5180527521642373.5180527521634fit!(m);
-
[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 550, minf = 2354.4744815688055)[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 567, minf = 2354.474481568814)
@@ -1202,7 +1202,7 @@
)
-
Converged to θ = 0.5683043594028967 and β =[-0.3409777149845993, 0.3933796201906975, 0.6064857599227369, -0.012926172564277872, 0.03323478854784157, -0.005626184982660486]Converged to θ = 0.5683043987329829 and β =[-0.3409777185006387, 0.39337972485653033, 0.606485842218137, -0.012926166672796164, 0.03323478753359014, -0.0056261864970479246]These estimates differ somewhat from those for model com05.
)
-Estimates for com05: θ = 0.5761507901895634, fmin = 2353.8241980539815, and β =[-0.3414913998306781, 0.3936080536502067, 0.6064861079468472, -0.012911714642169572, 0.03321662487439253, -0.005625046845040066]
+Estimates for com05: θ = 0.5761302648250215, fmin = 2353.8241975646893, and β =[-0.3414688923098128, 0.3935941398175495, 0.6064453377878877, -0.012909611190401555, 0.03321034920788019, -0.0056245886330953615]
Estimates for com05: θ = 0.5761507901895634, fmin = 2353.8241980539815, and β =[-0.3414913998306781, 0.3936080536502067, 0.6064861079468472, -0.012911714642169572, 0.03321662487439253, -0.005625046845040066]Estimates for com05: θ = 0.5761302648250215, fmin = 2353.8241975646893, and β =[-0.3414688923098128, 0.3935941398175495, 0.6064453377878877, -0.012909611190401555, 0.03321034920788019, -0.0056245886330953615]The discrepancy in the results is because the com05 results are based on a more accurate approximation to the integral called adaptive Gauss-Hermite Quadrature, which is discussed in Section C.6.
ev.values
5-element Vector{Float64}:
- -2.8569700138728
- -1.3556261799742608
- 1.3322676295501878e-15
- 1.3556261799742677
+ -2.8569700138728016
+ -1.3556261799742617
+ 8.881784197001252e-16
+ 1.3556261799742675
2.8569700138728056abs2.(ev.vectors[1, :])
5-element Vector{Float64}:
- 0.011257411327720667
- 0.2220759220056134
+ 0.01125741132772062
+ 0.22207592200561319
0.5333333333333334
0.222075922005612
0.011257411327720648
@@ -1341,7 +1341,7 @@
-
+
Figure C.3: Change in the penalized deviance contribution from that at the conditional mode, for each of the first 5 groups, in model com05, as a function of u.
@@ -1616,7 +1616,7 @@
-
+
Figure C.6: Exponential of half the difference between the quadratic approximation and the contribution to the penalized deviance, for each of first 5 groups in model com05 as a function of z.
@@ -1667,20 +1667,20 @@
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
abs2.(ev.vectors[1, :])5-element Vector{Float64}:
- 0.011257411327720667
- 0.2220759220056134
+ 0.01125741132772062
+ 0.22207592200561319
0.5333333333333334
0.222075922005612
0.011257411327720648
-
+
Figure C.3: Change in the penalized deviance contribution from that at the conditional mode, for each of the first 5 groups, in model com05, as a function of u.
@@ -1616,7 +1616,7 @@
-
+
Figure C.6: Exponential of half the difference between the quadratic approximation and the contribution to the penalized deviance, for each of first 5 groups in model com05 as a function of z.
@@ -1667,20 +1667,20 @@
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
-
+
+
-
+
Figure C.6: Exponential of half the difference between the quadratic approximation and the contribution to the penalized deviance, for each of first 5 groups in model com05 as a function of z.
@@ -1667,20 +1667,20 @@
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
-
+
+
extrema(m.utbl.aGHQ)
-(-0.008514108854172236, -0.0004132698576107887)
+(-0.008514109733813818, -0.000413268627218805)
extrema(m.utbl.aGHQ)(-0.008514108854172236, -0.0004132698576107887)(-0.008514109733813818, -0.000413268627218805)┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
+└ @ Main.Notebook ~/projects/EmbraceUncertainty/aGHQ.qmd:1212
┌ Warning: PIRLS iteration did not reduce penalized deviance
-└ @ Main.Notebook ~/Work/EmbraceUncertainty/aGHQ.qmd:1064
-[ Info: (ret = :ROUNDOFF_LIMITED, fevals = 479, minf = 2353.82419755322)7-element Vector{Float64}:
- 0.5761321679271924
- -0.3414655990254175
- 0.39359939391066806
- 0.6064447618771712
- -0.012909685721680265
- 0.03320994962034241
- -0.005624606329593786This page was rendered from git revision 31e9b61
+ This page was rendered from git revision 5657dd7
. The actual implementation of a row-table or column-table type may be different from these prototypes but it must provide access methods as if it were one of these types.
is a lightweight package (about 1500 lines of source code) that provides a concrete implementation of column-tables, called simply Tables.RowTable
-
+AbstractVector{T} where T<:NamedTuple (alias for AbstractArray{T, 1} where T<:NamedTuple)
+
AbstractVector{T} where T<:NamedTuple (alias for AbstractArray{T, 1} where T<:NamedTuple)
+Tables.jl provides the “glue” to treat a particular data table type as if it were row-oriented, by calling Tables.rows or Tables.rowtable on it, or column-oriented, by calling Tables.columntable on it.TypedTables.jl
Table, as a NamedTuple of vectors.
A Table that is constructed from another type of column-table, such as an Arrow.Table or a DataFrame or an explicit NamedTuple of vectors, is simply a wrapper around the original table’s contents. On the other hand, constructing a Table from a row table first creates a ColumnTable, then wraps it.
-
+
contratbl = Table(contra)contratbl = Table(contra)Table with 5 columns and 1934 rows:
dist urban livch age use
@@ -369,7 +371,7 @@
-typeof(contratbl)
+typeof(contratbl)
Table{@NamedTuple{dist::String, urban::String, livch::String, age::Float64, use::String}, 1, @NamedTuple{dist::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, urban::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, livch::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}, age::Arrow.DictEncoded{Float64, Int8, Arrow.Primitive{Float64, Vector{Float64}}}, use::Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}}}
@@ -381,7 +383,7 @@
-contratbl.urban
+contratbl.urban
1934-element Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}:
"Y"
@@ -408,14 +410,14 @@ Symbols, not strings, usually typed as a : followed by the name, as shown in
-columnnames(contratbl)
+columnnames(contratbl)
(:dist, :urban, :livch, :age, :use)
The : form for creating the Symbol requires that the column name be a valid variable name in Julia. If, for example, a column name contains a blank, the : form must be replaced by an expression like var"<name>", which invokes what is called a “string macro”.
-contratbl.var"urban"
+contratbl.var"urban"
1934-element Arrow.DictEncoded{String, Int8, Arrow.List{String, Int32, Vector{UInt8}}}:
"Y"
@@ -442,13 +444,13 @@
-contratbl[1]
+contratbl[1]
(dist = "D01", urban = "Y", livch = "3+", age = 18.44, use = "N")
-contratbl[2:5]
+contratbl[2:5]
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -466,7 +468,7 @@ A.3.2 A trivial example done several ways
Suppose we wish to select the rows from district D49 as a table. We could create a Boolean vector and use it to index into contratbl
-contratbl[contratbl.dist .== "D49"]
+contratbl[contratbl.dist .== "D49"]
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -495,8 +497,8 @@ .
-isD49dist(row) = row.dist == "D49" # a 'one-liner' function definition
-filter(isD49dist, contratbl)
+isD49dist(row) = row.dist == "D49" # a 'one-liner' function definition
+filter(isD49dist, contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -509,7 +511,7 @@
-filter(r -> r.dist == "D49", contratbl)
+filter(r -> r.dist == "D49", contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -522,7 +524,7 @@ .
-filter(==("D49") ∘ first, contratbl)
+filter(==("D49") ∘ first, contratbl)
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -551,7 +553,7 @@ generator expression
-Table(r for r in contratbl if r.dist == "D49")
+Table(r for r in contratbl if r.dist == "D49")
Table with 5 columns and 4 rows:
dist urban livch age use
@@ -565,10 +567,10 @@ Chapter 6 a newdata table is constructed from the Cartesian product of vectors of covariates as the newdata table.
-newdata = Table(
- (; age=a, ch=c, urban=u) # NamedTuple from iterator product
- for a in -10:3:20, c in [false, true], u in ["N", "Y"]
-)
+newdata = Table(
+ (; age=a, ch=c, urban=u) # NamedTuple from iterator product
+ for a in -10:3:20, c in [false, true], u in ["N", "Y"]
+)
Table with 3 columns and 44 rows:
age ch urban
@@ -607,7 +609,7 @@
In general a Tuple is written as a comma-separated set of values within parentheses.
-typeof((1, true, 'R'))
+typeof((1, true, 'R'))
Tuple{Int64, Bool, Char}
@@ -616,10 +618,10 @@
-newdata = Table(
- (; age, ch, urban) for age in -10:3:20, ch in [false, true],
- urban in ["N", "Y"]
-)
+newdata = Table(
+ (; age, ch, urban) for age in -10:3:20, ch in [false, true],
+ urban in ["N", "Y"]
+)
Table with 3 columns and 44 rows:
age ch urban
@@ -655,7 +657,7 @@ Chapter 6 we added a Boolean column, ch, indicating if livch is not "0", to the contra table using an expression like
-contratbl = Table(contratbl; ch=contratbl.livch .== "0")
+contratbl = Table(contratbl; ch=contratbl.livch .== "0")
Table with 6 columns and 1934 rows:
dist urban livch age use ch
@@ -682,9 +684,9 @@
-contratbl = Table(
- getproperties(contratbl, (:dist, :urban, :livch, :age, :use)),
-)
+contratbl = Table(
+ getproperties(contratbl, (:dist, :urban, :livch, :age, :use)),
+)
Table with 5 columns and 1934 rows:
dist urban livch age use
@@ -716,8 +718,8 @@ <
The JuliaData organization manages the development of several packages related to data science and data management, including DataFrames.jl, a comprehensive system for working with column-oriented data tables in Julia. Kamiński (2023), written by the primary author of that package, provides an in-depth introduction to data science facilities, in particular the DataFrames package, in Julia.
This package is particularly well-suited to more advanced data manipulation such as the split-apply-combine strategy (Wickham, 2011) and “joins” of data tables.
Bouchet-Valat & Kamiński (2023) compares the performance of DataFrames.jl to other data frame implementations in R and Python.
-This page was rendered from git revision 31e9b61
+This page was rendered from git revision 5657dd7
.
diff --git a/glmmbernoulli.html b/glmmbernoulli.html
index 25e5797..8cc1e20 100644
--- a/glmmbernoulli.html
+++ b/glmmbernoulli.html
@@ -534,18 +534,18 @@
(Intercept)
--0.0126
+-0.0125
0.1058
-0.12
-0.9052
+0.9061
0.4787
livch: 1
-0.1532
+0.1533
0.0982
1.56
-0.1188
+0.1185
@@ -558,7 +558,7 @@
livch: 3+
-0.2590
+0.2591
0.1022
2.53
0.0113
@@ -569,7 +569,7 @@ 0.0006
0.0095
0.07
-0.9466
+0.9479
@@ -582,7 +582,7 @@
urban: Y
-0.3770
+0.3771
0.0804
4.69
<1e-05
@@ -593,7 +593,7 @@ -0.0067
0.0069
-0.98
-0.3261
+0.3263
@@ -601,7 +601,7 @@ -0.0004
0.0007
-0.51
-0.6075
+0.6070
@@ -765,7 +765,7 @@
(Intercept)
--0.2194
+-0.2193
0.1155
-1.90
0.0576
@@ -784,7 +784,7 @@ 0.0035
0.0082
0.43
-0.6674
+0.6669
@@ -808,7 +808,7 @@ -0.0068
0.0069
-0.99
-0.3231
+0.3233
@@ -880,7 +880,7 @@
(Intercept)
--0.2302
+-0.2303
0.1140
-2.02
0.0434
@@ -888,7 +888,7 @@
urban: Y
-0.3461
+0.3462
0.0599
5.78
<1e-08
@@ -907,7 +907,7 @@ 0.0063
0.0078
0.80
-0.4249
+0.4247
@@ -1034,7 +1034,7 @@ -0.0131
0.0110
-1.19
-0.2351
+0.2352
@@ -1131,7 +1131,7 @@
ch: true
-0.6065
+0.6064
0.1045
5.80
<1e-08
@@ -1142,7 +1142,7 @@ -0.0129
0.0112
-1.16
-0.2470
+0.2471
@@ -1174,29 +1174,29 @@
Generalized Linear Mixed Model fit by maximum likelihood (nAGQ = 9)
use ~ 1 + urban + ch + age + :(abs2(age)) + ch & age + (1 | dist & urban)
- Distribution: Bernoulli{Float64}
- Link: LogitLink()
+ Distribution: Distributions.Bernoulli{Float64}
+ Link: GLM.LogitLink()
logLik deviance AIC AICc BIC
-1177.2418 2353.8242 2368.4836 2368.5418 2407.4550
Variance components:
Column Variance Std.Dev.
-dist & urban (Intercept) 0.331927 0.576131
+dist & urban (Intercept) 0.331929 0.576133
Number of obs: 1934; levels of grouping factors: 102
Fixed-effects parameters:
-─────────────────────────────────────────────────────────
- Coef. Std. Error z Pr(>|z|)
-─────────────────────────────────────────────────────────
-(Intercept) -0.341486 0.126906 -2.69 0.0071
-urban: Y 0.393595 0.0859086 4.58 <1e-05
-ch: true 0.606464 0.104531 5.80 <1e-08
-age -0.0129123 0.0111549 -1.16 0.2470
-abs2(age) -0.00562457 0.000844101 -6.66 <1e-10
-ch: true & age 0.0332117 0.0128228 2.59 0.0096
-─────────────────────────────────────────────────────────
+────────────────────────────────────────────────────────
+ Coef. Std. Error z Pr(>|z|)
+────────────────────────────────────────────────────────
+(Intercept) -0.341466 0.126905 -2.69 0.0071
+urban: Y 0.393594 0.0859087 4.58 <1e-05
+ch: true 0.606442 0.104529 5.80 <1e-08
+age -0.0129098 0.0111548 -1.16 0.2471
+abs2(age) -0.00562462 0.0008441 -6.66 <1e-10
+ch: true & age 0.0332098 0.0128227 2.59 0.0096
+────────────────────────────────────────────────────────
Notice that, although there are 60 distinct districts, there are only 102 distinct combinations of dist and urban represented in the data. In 15 of the 60 districts there are no rural women in the sample and in 3 districts there are no urban women in the sample, as shown in a frequency table
@@ -1307,23 +1307,23 @@ Table with 4 columns and 44 rows:
age ch urban η
┌─────────────────────────────
- 1 │ -10 false N -1.44276
- 2 │ -7 false N -1.29428
- 3 │ -4 false N -1.24704
- 4 │ -1 false N -1.30104
- 5 │ 2 false N -1.45629
- 6 │ 5 false N -1.71278
- 7 │ 8 false N -2.07051
- 8 │ 11 false N -2.52948
- 9 │ 14 false N -3.0897
- 10 │ 17 false N -3.75115
- 11 │ 20 false N -4.51385
- 12 │ -10 true N -0.894068
- 13 │ -7 true N -0.546316
- 14 │ -4 true N -0.299807
- 15 │ -1 true N -0.15454
+ 1 │ -10 false N -1.44277
+ 2 │ -7 false N -1.29427
+ 3 │ -4 false N -1.24702
+ 4 │ -1 false N -1.30101
+ 5 │ 2 false N -1.45624
+ 6 │ 5 false N -1.71271
+ 7 │ 8 false N -2.07043
+ 8 │ 11 false N -2.5294
+ 9 │ 14 false N -3.0896
+ 10 │ 17 false N -3.75105
+ 11 │ 20 false N -4.51374
+ 12 │ -10 true N -0.89408
+ 13 │ -7 true N -0.546324
+ 14 │ -4 true N -0.299812
+ 15 │ -1 true N -0.154542
16 │ 2 true N -0.110516
- 17 │ 5 true N -0.167734
+ 17 │ 5 true N -0.167733
⋮ │ ⋮ ⋮ ⋮ ⋮
@@ -1346,7 +1346,7 @@
-
+
Figure 6.3: Linear predictor versus centered age from model com05
@@ -1411,23 +1411,23 @@ <
Table with 5 columns and 44 rows:
age ch urban η μ
┌────────────────────────────────────────
- 1 │ -10 false N -1.44276 0.191118
- 2 │ -7 false N -1.29428 0.215129
- 3 │ -4 false N -1.24704 0.223213
- 4 │ -1 false N -1.30104 0.213989
- 5 │ 2 false N -1.45629 0.189035
- 6 │ 5 false N -1.71278 0.152804
- 7 │ 8 false N -2.07051 0.111996
- 8 │ 11 false N -2.52948 0.0738171
- 9 │ 14 false N -3.0897 0.0435342
- 10 │ 17 false N -3.75115 0.0229515
- 11 │ 20 false N -4.51385 0.0108374
- 12 │ -10 true N -0.894068 0.290271
- 13 │ -7 true N -0.546316 0.366719
- 14 │ -4 true N -0.299807 0.425605
- 15 │ -1 true N -0.15454 0.461442
+ 1 │ -10 false N -1.44277 0.191117
+ 2 │ -7 false N -1.29427 0.215131
+ 3 │ -4 false N -1.24702 0.223217
+ 4 │ -1 false N -1.30101 0.213996
+ 5 │ 2 false N -1.45624 0.189043
+ 6 │ 5 false N -1.71271 0.152812
+ 7 │ 8 false N -2.07043 0.112004
+ 8 │ 11 false N -2.5294 0.073823
+ 9 │ 14 false N -3.0896 0.0435383
+ 10 │ 17 false N -3.75105 0.0229538
+ 11 │ 20 false N -4.51374 0.0108386
+ 12 │ -10 true N -0.89408 0.290269
+ 13 │ -7 true N -0.546324 0.366718
+ 14 │ -4 true N -0.299812 0.425604
+ 15 │ -1 true N -0.154542 0.461441
16 │ 2 true N -0.110516 0.472399
- 17 │ 5 true N -0.167734 0.458164
+ 17 │ 5 true N -0.167733 0.458165
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮
@@ -1450,7 +1450,7 @@ <
-
+
Figure 6.5: Predicted probability of contraception use versus centered age from model com05.
@@ -1466,10 +1466,10 @@ <
Table with 5 columns and 4 rows:
age ch urban η μ
┌───────────────────────────────────────
- 1 │ 2 false N -1.45629 0.189035
+ 1 │ 2 false N -1.45624 0.189043
2 │ 2 true N -0.110516 0.472399
- 3 │ 2 false Y -0.669101 0.338698
- 4 │ 2 true Y 0.676673 0.662996
+ 3 │ 2 false Y -0.669052 0.338709
+ 4 │ 2 true Y 0.676672 0.662995
The predicted probability of woman with centered age of 2, with children, living in an urban environment using artificial contraception is about 2/3, which is reasonably close to the smoothed frequency for that combination of covariates in Figure 6.2.
@@ -1487,7 +1487,7 @@
-
+
Figure 6.6: Caterpillar plot of the conditional modes of the random-effects for model com05
@@ -1506,12 +1506,12 @@ Table with 2 columns and 6 rows:
dist & urban (Intercept)
┌──────────────────────────
- 1 │ ("D01", "N") -0.957366
- 2 │ ("D11", "N") -0.93198
- 3 │ ("D24", "N") -0.603418
+ 1 │ ("D01", "N") -0.957367
+ 2 │ ("D11", "N") -0.931983
+ 3 │ ("D24", "N") -0.60342
4 │ ("D01", "Y") -0.580203
- 5 │ ("D27", "N") -0.576647
- 6 │ ("D55", "Y") -0.548261
+ 5 │ ("D27", "N") -0.576648
+ 6 │ ("D55", "Y") -0.548263
@@ -1520,12 +1520,12 @@ Table with 2 columns and 6 rows:
dist & urban (Intercept)
┌──────────────────────────
- 1 │ ("D43", "N") 0.64408
- 2 │ ("D04", "Y") 0.644669
- 3 │ ("D42", "N") 0.665114
- 4 │ ("D58", "N") 0.677418
+ 1 │ ("D43", "N") 0.644081
+ 2 │ ("D04", "Y") 0.644671
+ 3 │ ("D42", "N") 0.665117
+ 4 │ ("D58", "N") 0.67742
5 │ ("D14", "Y") 0.695322
- 6 │ ("D34", "N") 1.08591
+ 6 │ ("D34", "N") 1.08592
The largest random effect is for rural settings in D34. There were 26 women in the sample from rural D34
@@ -1565,12 +1565,12 @@
exp(last(first(srtdre)))
-0.38390287360272524
+0.3839023558380497
or about 40%.
-This page was rendered from git revision 31e9b61
+This page was rendered from git revision 5657dd7
.
diff --git a/index.html b/index.html
index f8ffd96..0ed055f 100644
--- a/index.html
+++ b/index.html
@@ -9,7 +9,7 @@
-
+
Embrace Uncertainty